A double atari is a play that puts two groups of stones into atari, i.e. it reduces the two groups to one liberty each.
White is a double atari. It reduces both marked black groups to one liberty. Black can only save one of his marked groups.
Failure to see a double atari can be very costly in games.
(Dansol in Korean, I believe. In Japanese it is ryouatari.)
BenAxelrod - This is a very simple way to get a double atari. As a beginner, playing against mostly other beginners, I see it a lot.
Protect the middle of three double ataris